「あなたは学生なんだ。」my main point to emphasize here is the use of 「んだ」。 I did a little research and i found out it is derived from のだ。 can someone please explain to me in more detail how this grammar works?

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That's the difficult point to explain. lol

You are a student, so you can use a student discount.
あなたは学生だから、学割が使えます。

You are a student, so you should buy books before a car.
あなたは学生なんだから、車を買うより本を買いなさい。

In these cases, なんだ is used to emphasize "you are a student".
Impring "you are nothing but a student, nor a established nor a manager in a company."

んだ（のだ） is often used to show the point of the speech/sentence. But not always.
People always choose んだ to start talking something.

きのうネットで見たんだけどさ、

in this case he/she implies nothing. Only means to bring on a new topic for the small talk.

When you translate Japanese speech into English, you need not mind the difference between だ and んだ.
But in the opposite translations, んだ matters a lot, I guess. Too many and too less んだ both make it quite unnatural.